Skorohod representation on a given probability space

Let $(\Omega,\mathcal{A},P)Let be a probability space, S a metric space, μ a probability measure on the Borel σ-field of S, and an arbitrary map, n = 1,2,.... If μ is tight and X _n converges in distribution to μ (in Hoffmann–J?rgensen’s sense), then X∼μ for some S-valued random variable X on . If, in addition, the X _n are measurable and tight, there are S-valued random variables and X, defined on , such that , X∼μ, and a.s. for some subsequence (n _k ). Further, a.s. (without need of taking subsequences) if μ{x} = 0 for all x, or if P(X _n = x) = 0 for some n and all x. When P is perfect, the tightness assumption can be weakened into separability up to extending P to for some H⊂Ω with P ^*(H) = 1. As a consequence, in applying Skorohod representation theorem with separable probability measures, the Skorohod space can be taken , for some H⊂ (0,1) with outer Lebesgue measure 1, where is the Borel σ-field on (0,1) and m _H the only extension of Lebesgue measure such that m _H (H) = 1. In order to prove the previous results, it is also shown that, if X _n converges in distribution to a separable limit, then X _{n k} converges stably for some subsequence (n _k ).      

An egg-yolk principle and exponential integrability for quasiregular mappings

Quasiregular mappings f:ⁿⁿ are a natural generalization of analyticfunctions from complex analysis and provide a theory which isrich with new phenomena. In this paper we extend a well-knownresult of Chang and Marshall on exponential integrability ofanalytic functions in the disk, to the case of quasiregularmappings defined in the unit ball of ⁿ. To this end, an ‘egg-yolk’principle is first established for such maps, which extendsa recent result of the first author. Our work leaves open aninteresting problem regarding n-harmonic functions.     

Ab initio molecular dynamics study of the hydrolysis reaction of diborane

The hydrolysis reaction of the diborane molecule in aqueous solution has been studied by a series of Car-Parrinello Molecular Dynamics simulations in the Blue Moon Ensemble. The total reaction has been divided into two parts: one dealing with the breaking of B(2)H(6) molecule and the formation of a BH(4)(-) ion, a H(2)BOH molecule and a H(+) ion; the second leads to the formation of two hydrogen molecules and another H(2)BOH molecule, starting from BH(4)(-), two water molecules and a H(+) ion. The total reaction studied in this work has been B(2)H(6) + 2H(2)O --> 2H(2)BOH + 2H(2). We have described both structurally and electronically the reagents and the products through the radial distribution functions and the Wannier Function Center positions calculations, with attention to the solvent effects on the compounds. The free energy barrier value for the first part of the reaction and a detailed mechanisms for both parts have been reported. An interesting behavior of BH(3) and H(2) molecules in solution has been observed. They form a quite stable three center bond between the electron pair of the hydrogen molecule and the empty orbital of the boron atom in BH(3), which has been described from both a structural and electronic point of view.     

Curvature driven transport of mouse macrophages in a pulsating magnetic garnet film ratchet

Magnetic fields varying on the colloidal length scale are used for the directed transport of magnetically labeled biological cells. The transport is achieved by using the ratchet effect which relies on an asymmetric, symmetry broken periodic potential where nonequilibrium fluctuations or oscillations generate a net cell current. Ferrofluid ingested mouse macrophages were placed on a magnetic garnet film with alternating stripe domain patterns, and a pulsating magnetic potential is provided by superposing an oscillating magnetic field normal to the film. The symmetry of the resulting periodic stripe potential is broken locally by the curvature of the stripes. We show, both experimentally and theoretically, the curvature of such stripes required for inducing directed transport of the macrophages in the ratchet. This may be useful for microfluidic devices such as a digital colloidal shift register for magnetically labeled biological cells.     

Mapping properties of analytic functions on the disk

There is a universal constant with the following property. Suppose that is an analytic function on the unit disk , and suppose that there exists a constant so that the Euclidean area, counting multiplicity, of the portion of which lies over the disk , centered at and of radius , is strictly less than the area of . Then must send into . This answers a conjecture of Don Marshall.

     

Multivariate analysis of matrix-assisted laser desorption/ionization mass spectrometric data related to glycoxidation products of human globins in nephropathic patients

To clarify the possible pathogenetic role of oxidation products originated from the glycation of proteins, human globins from nephropathic patients have been studied by matrix-assisted laser desorption/ionization mass spectrometry (MALDI), revealing not only unglycated and monoglycated globins, but also a series of different species. For the last ones, structural assignments were tentatively done on the basis of observed masses and expectations for the Maillard reaction pattern. Consequently, they must be considered only propositive, and the discussion which will follow must be considered in this view. In our opinion this approach does not seem to compromise the intended diagnostic use of the data because distinctions are valid even if the assignments are uncertain. We studied nine healthy subjects and 19 nephropathic patients and processed the data obtained from the MALDI spectra using a multivariate analysis. Our results showed that multivariate analytical techniques enable differential aspects of the profile of molecular species to be identified in the blood of end stage nephropathic patients. A correct grouping can be achieved by principal component analysis (PCA) and the results suggest that several products involved in carbonyl stress exist in nephropathic patients. These compounds may have a relevant role as specific markers of the pathological state.     

Localized and delocalized motion of colloidal particles on a magnetic bubble lattice

We study the motion of paramagnetic colloidal particles placed above magnetic bubble domains of a uniaxial garnet film and driven through the lattice by external magnetic field modulation. An external tunable precessing field propels the particles either in localized orbits around the bubbles or in superdiffusive or ballistic motion through the bubble array. This motion results from the interplay between the driving rotating signal, the viscous drag force and the periodic magnetic energy landscape. We explain the transition in terms of the incommensurability between the transit frequency of the particle through a unit cell and the modulation frequency. Ballistic motion dynamically breaks the symmetry of the array and the phase locked particles follow one of the six crystal directions.     

Direct solvothermal synthesis of early transition metal nitrides

Solvothermal reactions of TaCl5 with LiNH2 in benzene result in nanocrystalline Ta3N5 at 500 or 550 degrees C. The approximately 25 nm Ta3N5 particles have a band gap of 2.08-2.10 eV. The same reactions in mesitylene resulted in a higher crystallization temperature and large amounts of carbon incorporation due to solvent decomposition. Reactions of Ta(NMe2)5 with LiNH2 under the same conditions resulted in TaN. Rocksalt-type MN phases are obtained for Zr, Hf, or Nb when their chlorides (ZrCl4, HfCl4, or NbCl5) or dialkylamides (M(NEtMe)4, M = Zr, Hf) are reacted with LiNH2 under similar conditions. With the amides, there is some evidence for nitrogen-rich compositions (HfN >1), and carbon is incorporated into the products through pyrolysis of the dialkylamide groups.